A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily; Donal O'Regan

doi:10.1016/j.nonrwa.2005.06.008

A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Mohamed El-Gebeily
, Donal O'Regan

Mathematics

King Fahd University of Petroleum and Minerals

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

23 Citations (Scopus)

Abstract

We consider the differential equation - (1 / w) (pu^′)^′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

Original language	English
Pages (from-to)	174-186
Number of pages	13
Journal	Nonlinear Analysis: Real World Applications
Volume	8
Issue number	1
DOIs	https://doi.org/10.1016/j.nonrwa.2005.06.008
Publication status	Published - 1 Feb 2007

Keywords

Nonlinear boundary conditions
Nonlinear ordinary differential equations
Quasilinearization method
Upper and lower solutions

Authors (Note for portal: view the doc link for the full list of authors)

Authors
El-Gebeily, M;O'Regan, D

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10.1016/j.nonrwa.2005.06.008

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abstract = "We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.",

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N2 - We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

AB - We consider the differential equation - (1 / w) (pu′)′ + μ u = Fu, where F is a nonlinear operator, with nonlinear boundary conditions. Under appropriate assumptions on p, w, F and the boundary conditions, the existence of solutions is established. If the problem has a lower solution and an upper solution, then we use a quasilinearization method to obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.

KW - Nonlinear boundary conditions

KW - Nonlinear ordinary differential equations

KW - Quasilinearization method

KW - Upper and lower solutions

UR - https://www.scopus.com/pages/publications/33750064584

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DO - 10.1016/j.nonrwa.2005.06.008

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JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions

Abstract

Keywords

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